NORTH SOUTH UNIVERSITY TUTORIAL 1

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1 NORTH SOUTH UNIVERSITY TUTORIAL 1 REVIEW FROM BIOSTATISTICS I AHMED HOSSAIN,PhD Data Management and Analysis AHMED HOSSAIN,PhD - Data Management and Analysis 1

2 DATA TYPES/ MEASUREMENT SCALES Categorical: Nominal and Ordinal Quantitive (Interval/ Ratio): Discrete data and Continuous NOMINAL ORDINAL DISCRETE DATA Nominal data arises in measurements whose values fall into categories that have no natural numerical value. Nominal data often coded numerically, but the codes are just alternate names. For example, 0 for female and 1 for male. Ordinal data fall into categories that can be qualitatively ordered, but have no intrinsic numerical value. Ordinal data can be ranked. For example, education or economic status. measured quantities that take on specific values, usually integers. For example, number of traffic accidents, number of infant deaths etc. CONTINUOUS DATA measured quantities not restricted to specific values. For example, Birth weight, Cholesterol level, blood pressure etc. AHMED HOSSAIN,PhD - Data Management and Analysis 2

3 DATA SUMMARIES Tabular: Frequencies, relative frequencies etc. Graphical: Bar charts, histograms, scatter plots, box plots etc. FREQUENCY TABLES Frequency Tables used to summarize Nominal or ordinal data having natural categories Discrete or continuous data, usually after data have been grouped into categories AHMED HOSSAIN,PhD - Data Management and Analysis 3

4 DATA SUMMARIES: BIVARIATE TABLE AHMED HOSSAIN,PhD - Data Management and Analysis 4

5 DATA SUMMARIES: BIVARIATE TABLE Variables Complication level 2 -value p.value Categories No Yes Sex F M Marital status Married Unmarried 4 14 Other Health Problems No Yes Family History Negative Positive Smoking No Yes AHMED HOSSAIN,PhD - Data Management and Analysis 5

6 DATA SUMMARIES: BARPLOT Find a limitation of this barplot. It is in terms of interpretation. Studetns with Visual Acuity corresponds to Parents myopia Number of Studetns Fair Good No Yes AHMED HOSSAIN,PhD - Data Management and Analysis 6

7 DATA SUMMARIES: HISTOGRAM AHMED HOSSAIN,PhD - Data Management and Analysis 7

8 DATA SUMMARIES: HISTOGRAM AHMED HOSSAIN,PhD - Data Management and Analysis 8

9 DATA SUMMARIES: HISTOGRAM AHMED HOSSAIN,PhD - Data Management and Analysis 9

10 DATA SUMMARIES: HISTOGRAM AHMED HOSSAIN,PhD - Data Management and Analysis 10

11 DATA SUMMARIES: BOX PLOT AHMED HOSSAIN,PhD - Data Management and Analysis 11

12 DATA SUMMARIES: BOX PLOT AHMED HOSSAIN,PhD - Data Management and Analysis 12

13 DATA SUMMARIES: BOX PLOT AHMED HOSSAIN,PhD - Data Management and Analysis 13

14 DATA SUMMARIES: COMPARING BOX PLOTS Boxplot of Age Boxplot of BMI Age BMI No Yes No Yes Compliance Level Compliance Level AHMED HOSSAIN,PhD - Data Management and Analysis 14

15 DATA SUMMARIES: LOCATION AND SHAPE MEASURES OF CENTRAL TENDENCY Mean, Median and Mode. MEASURES OF SPREAD Range, Interquartile range, variance and standard deviation. AHMED HOSSAIN,PhD - Data Management and Analysis 15

16 DATA SUMMARIES: STANDARD DEVIATION TABLE: Descriptions of Age and BMI corresponds to LBP LBP lasted for 1 day Chronic LBP Intense pain Yes No Yes No Yes No Age 34.72(8.21) 30.37(6.69) 37.79(7.81) 31.55(7.37) 37.79(7.47) 32.26(7.83 BMI 23.95(3.43) 22.00(2.97) 24.36(3.02) 22.99(3.52) 24.98(3.33) 22.92(3.30 AHMED HOSSAIN,PhD - Data Management and Analysis 16

17 PROBABILITY DEFN Have you ever asked what are the chances?, if you have, you were asking a probabiliy question. Remember, the probability of an event is its long run relative frequency. AHMED HOSSAIN,PhD - Data Management and Analysis 17

18 DISCRETE PROBABILITY DISTRIBUTIONS EXAMPLE Hyponatremia (low sodium levels) occurs in a certain proportion of marathon runners. Now the question is, how many cases of hyponatremia are expected during the running of a particular marathon? What do you need to know to answer this question? Suppose there are 200 runners participating in a marathon (n = 200). Suppose historically the proportion of runners who develop hyponatremia is assumed to be 0.12 (p = 0.12). Let X denote the number of these runners who develop hyponatremia. Then X follows binomial random variable. AHMED HOSSAIN,PhD - Data Management and Analysis 18

19 CONTINUOUS: NORMAL DISTRIBUTION Normal (Gaussian) distribution is everywhere: stock market fluctuations, heights, temperatures, IQ scores, etc. Normal density is an accurate approximation to the binomial probability function for large n. AHMED HOSSAIN,PhD - Data Management and Analysis 19

20 DISTRIBUTION OF SAMPLE MEAN AND CONFIDENCE INTERVAL CENTRAL LIMIT THEOREM The Central Limit Theorem states that distribution of X has mean µ and standard error p n which follows normal (Gaussian) as n becomes large, regardless of the distribution of X. CONFIDENCE INTERVAL The 95% confidence interval for the populaiton mean µ is given by X 1.96 p, X p n n Provides an estimate of a population mean along with a margin of error. Has an associated level of confidence, or probability that the interval contains population mean in repeated sampling. Find out the distribution for proportions and its 95% confidence intervals. AHMED HOSSAIN,PhD - Data Management and Analysis 20

21 HYPOTHESIS TESTING Sometimes it is useful to make a statement about whether a population mean has a hypothesized value, with associated probabilities of error. For example, do hypertensive, smoking men have same mean cholesterol level as in general population? or, do children who have experienced cardiac surgery have mean IQ scores the same as population norms (µ = 100)? etc. 1 The null hypothesis for the cholesterol example, H 0 : µ = 211mg/100 ml. and in the IQ example, H 0 : µ = The alternative hypothesis for the cholesterol example, H 0 : µ 6= 211mg/100 ml. (two sided) and in the IQ example, H 0 : µ<100 (one sided). 3 Then choose the significance level which is the acceptable error probability of the test. Typically, is taken to be 0.05, 0.01, or some other small value. 4 Calculate the value of the test statistic on which the test will be based. The test statistic will be either a z-statistic, if the population standard deviation is known or a t-statistic, if the population standard deviation is not known. 5 Calculate the p-value (probability value) of the observed result. The smaller the p-value, the stronger the evidence against the null hypothesis. AHMED HOSSAIN,PhD - Data Management and Analysis 21

22 OTHER IMPORTANT DISTRIBUTIONS POISSON t This discrete distribution helps to find the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. For example, the number of phone calls received by a call center per hour. This continous distribution is used where the sample size is small and population standard deviation is unknown. 2 The chi-squared distribution is used in the common 2 tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. F The F distribution arises frequently as the null distribution of a test statistic, most notably in the analysis of variance. AHMED HOSSAIN,PhD - Data Management and Analysis 22

23 WHICH STATISTICAL TEST SHOULD I USE? AHMED HOSSAIN,PhD - Data Management and Analysis 23

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28 R FOR WINDOWS AHMED HOSSAIN,PhD - Data Management and Analysis 24

29 EXPLORATORY ANALYSIS: R AHMED HOSSAIN,PhD - Data Management and Analysis 25